Messing around with the Crouching Tiger Hidden Dragon 4k disc (I will properly rewatch the film at some point) and fascinated to learn that it swaps out the opening logos and the language of the ending song depending on which subtitle option you pick - with English subtitles selected there's a Sony Pictures Classics logo at the start and an English language ending song (even though it's otherwise the Mandarin audio) and without subtitles it's the Columbia Pictures logo at the start and the Mandarin version of the ending.
This feels like a lot of effort to go to, tbh. The old US DVD (and the regular Blu-ray as far as I'm aware) just always had the Sony Pictures Classics logo at the start and the Mandarin ending song (but the English one on the dub audio track). Someone had to cue up some complicated branching code just to make sure nobody was upset by seeing the logo from the wrong Sony division
Edit: so the old Blu-ray that's bundled with my 4K just had the Columbia Pictures logo at the start but based on the languages included my copy of the Blu-ray is a European-focussed master and the US DVD definitely had the Sony Classics logo, so the US Blu-ray may differ. I think there's also a later pressing of the 4K in the US that has Dolby Vision so I wonder if that's still like this. Also, the menus on all these discs are overengineered and laggy!